The Singular Limit of a Chemotaxis-Growth System with General Initial Data

TL;DR

This paper investigates the singular limit of a chemotaxis-growth PDE system, revealing interface generation, motion by mean curvature, and precise estimates of transition layer properties for general initial data.

Contribution

It introduces a comprehensive analysis of the singular limit for a chemotaxis-growth model with general initial data, including interface dynamics and layer estimates.

Findings

Interface generation is proven under broad initial conditions.

The interface moves according to mean curvature with a nonlocal drift.

Optimal bounds on transition layer thickness and location are established.

Abstract

We study the singular limit of a system of partial differential equations which is a model for an aggregation of amoebae subjected to three effects: diffusion, growth and chemotaxis. The limit problem involves motion by mean curvature together with a nonlocal drift term. We consider rather general initial data. We prove a generation of interface property and study the motion of interfaces. We also obtain an optimal estimate of the thickness and the location of the transition layer that develops.